Flow restrictor and system for delivering a flow of liquid in a microcapillary

ABSTRACT

The present invention relates to apparatus for delivering a controlled or restricted flow of liquid and limiting bubble fragmentation at the inlet. This is achieved in flow restrictor with a flow channel having over most of its length a substantially constant, minimum hydraulic diameter D=4A/W wherein A is the minimum local cross-sectional area of the channel and W is the minimum local wetting perimeter of the channel, by smoothly widening the channel at its inlet such that: 
         at distances z from the inlet face with 0&lt;z&lt;z 1 , the channel has a hydraulic diameter D z ≧k*D wherein k≧1.3;    at distances z from the inlet face with z 1 &lt;z&lt;z 2 , the channel has a hydraulic diameter D z  with k*D≧D z ≧D; and    at distances z from the inlet face with z 2 &lt;z, the channel has a hydraulic diameter D z  with D z ≦1.02D, except possibly for a similar widening of the channel at the outlet. It has been found that widening the flow channel at the inlet, such that its diameter increases smoothly and gradually, and preferably by a factor of at least 1.3 over a length of at least 3 channel diameters, significantly reduces the tendency towards bubble fragmentation in microcapillary flow restrictors, and also substantially increases the yield of devices which operate well.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is entitled to the benefit of and incorporates byreference essential subject matter disclosed in International PatentApplication No. PCT/DK2004/000587 filed on Sep. 4, 2004 and DanishPatent Application No. PA 2003 01301 filed Sep. 10, 2003.

FIELD OF THE INVENTION

The present invention relates to apparatus for delivering a controlledor restricted flow of liquid. An example of such apparatus is aninfusion pump for delivering a controlled flow of medication to apatient during a certain period of time which can be a number of days.Other applications might be envisaged in the chemical or biotechnologyfields.

BACKGROUND OF THE INVENTION

In medical infusion, the flow typically needs to be restricted to ratherlow rates, such as, for example, 1000 microlitres per hour. Delivery ofliquids at flow rates of a few millilitres per hour or less may berealized by connecting a source of pressurized liquid to a capillary ofsmall internal diameter. In capillaries the rate of flow through thecapillary has a well-defined relation to the length and diameter of thecapillary, and to the difference in pressure between the capillary inletand the capillary outlet. For any given pressure difference the flowrate may thus be fixed at a desired value by choosing a capillary ofsuitable length and diameter.

A problem with capillaries of very small internal diameter(microcapillaries) is that bubbles of gas in the liquid may have aserious impact on the pressure difference or pressure drop required todrive a given flow rate through the capillary, and in the worst casebubbles may lead to an effective blocking of the capillary. This is dueto the phenomenon of fragmentation of a (larger) bubble at the inlet ofthe capillary into a plurality of small bubbles within the capillary.The small bubbles are separated from each other by plugs of liquid, andeach small bubble requires a certain pressure difference between itsends to move along the capillary. That pressure difference is largelyindependent of bubble length. Bubble fragmentation at the inlet may fillthe capillary with so many small bubbles that the pressure differenceavailable for generating liquid flow is reduced or fully consumed by thesum of pressure drops needed to drive the small bubbles along thecapillary. Therefore, flow through the capillary may be severely reducedor even stopped by bubble fragmentation.

Fused silica microcapillaries with an internal diameter of 10 to 100micrometers are widely used in the field of chemical analysis, inapplications such as capillary electrophoresis and gas chromatography.Microcapillary flow restrictors for use in medical infusion are easilymade by cutting suitable lengths (a few centimeters each) off from fusedsilica microcapillary stock. Other choices of material are alsoavailable, such as polymeric capillaries or micromachined planarcapillary structures.

Unfortunately, however, experience shows that the occurrence of bubblefragmentation in microcapillary flow restrictors is not predictable. Outof 100 flow restrictors made, some may have a very low tendency towardsbubble fragmentation whereas others will fragment virtually any bubblethat enters. There is a lack of yield and a lack of predictability. Bothare major obstacles in the industrial use of microcapillary flowrestrictors, for example in mass fabrication of medical infusiondevices.

BRIEF SUMMARY OF THE INVENTION

It is an object of the present invention to devise a flow restrictorstructure which has less tendency towards bubble fragmentation, which ismore predictable in its bubble fragmentation behaviour and whichprovides a higher yield of usable devices than commonly knownmicrocapillary flow restrictors.

This is achieved in flow restrictor with a flow channel having over mostof its length a substantially constant, minimum hydraulic diameterD=4A/W wherein A is the minimum local cross-sectional area of thechannel and W is the minimum local wetting perimeter of the channel, bysmoothly widening the channel at its inlet such that:

at distances z from the inlet face with 0<z<z₁, the channel has ahydraulic diameter D_(z)≧k*D wherein k≧1.3;

at distances z from the inlet face with z₁<z<z₂, the channel has ahydraulic diameter D_(z) with k*D≧D_(z)≧D; and

at distances z from the inlet face with z₂<z, the channel has ahydraulic diameter D_(z) with D_(z)≦1.02D, except possibly for a similarwidening of the channel at the outlet.

It has been found that widening the flow channel at the inlet, such thatits diameter increases smoothly and gradually, and preferably by afactor of at least 1.3 over a length of at least 3 channel diameters,significantly reduces the tendency towards bubble fragmentation inmicrocapillary flow restrictors, and also substantially increases theyield of devices which operate well.

BRIEF DESCRIPTION OF THE DRAWINGS

A preferred embodiment of the invention will now be described in detailwith reference to the drawings:

FIG. 1 is a flow restrictor made by cutting a length off frommicrocapillary stock; and in

FIG. 2 is a flow restrictor made by gradually widening the internaldiameter of a microcapillary at the inlet, in accordance with theinvention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows a capillary flow restrictor 10 made by cutting off a lengthof microcapillary which is commercially available from various vendorsfor use in the field of chemical analysis (gas chromatography, capillaryelectrophoresis etc).

The device 10 is an elongated tube whose wall 1 is made from fusedsilica (quartz glass) with an outer cladding 2 of polyimide. The wall 1surrounds a flow channel 3 of circular or rectangular (for example,square) cross-section which extends from an inlet 4 to an outlet 5. Atthe inlet, the flow channel 3 forms an inlet opening 6 in an inlet face7 of the flow restrictor, and at the outlet it forms an outlet opening 8in an outlet face 9 of the flow restrictor. Depending on how the devicewas cut off, the inlet face 7 and the outlet face 9 of the device may besmooth (from abrasive cutting) as shown at 7 or slightly rough (fromscoring and breaking) as shown at 9.

The flow restrictor 10 is mounted in a flow system for delivering acontrolled flow of liquid from a source 12 of liquid 14 to a recipient13. The source 12 is pressurized in a suitable way, not shown, to apressure which his higher than the pressure prevailing at the recipient13. For example, in a medical infusion system the source 12 may be aninflated bladder at a pressure of about 300-2000 mbar above recipientpressure, and the recipient 13 may be a blood vessel or any othersuitable internal location in the body of a patient who has received theentire flow system as an implant.

Mounting detail is schematically indicated at both ends of the flowrestrictor, where the polyimide cladding has been removed to allowdirect contact between a fluid-tight clamping system, indicated as 11,and the body 1 of the capillary tube.

The liquid 14 may contain bubbles of gas 15. One such bubble 16 is shownas being driven into the inlet 4 of the flow channel 3 by the pressuredifference between source and recipient. Often the presence of thebubble causes two-phase flow at the channel inlet 4. Liquid flows in athin layer 17 which adheres to the inner surface of the channel 3. Theliquid layer 17 coaxially surrounds a flow 18 of gas which fills theremaining core of the channel 3.

The two-phase flow in the flow channel 3 exhibits a phenomenon ofinstability, which frequently leads to fragmentation of the gas flowinto separate bubbles 18 of gas separated by plugs 19 of liquid. This isdue to the surface tension of the liquid-gas interface of the film 17.The surface tension causes a tendency of the liquid film to reduce itssurface. Perturbations having a wavelength longer than π*D (where D isthe hydraulic diameter of the channel as defined earlier) may grow untila bubble is pinched off as indicated at 20 and 21. Such fragmentation isfrequently observed, although its onset has turned out in practice to belargely unpredictable. It leads to the generation of a plurality ofsmall bubbles each having a length L_(min) of the order of the wettedperimeter of the channel, π*D.

As is commonly known, the flow of liquid through the channel 3 followsthe law of Hagen-Poiseuille: $\begin{matrix}{Q = \frac{{\partial D^{4}}Ä\quad P}{128ç_{1}L}} & (1)\end{matrix}$wherein Q is the flow rate, D is the hydraulic diameter of the flowchannel, ΔP is the pressure difference between the inlet and the outletof the flow channel, L is the length of the flow channel and η_(l) isthe viscosity of the liquid. Rearranging equation (1) we get$\begin{matrix}{{Ä\quad P} = \frac{128Q\quad ç_{1}L}{\partial D^{4}}} & (2)\end{matrix}$as an expression indicating the pressure drop required to drive the flowrate Q of liquid through the channel 3.

In the case of a flow of gas through the channel 3, the same expression(2) would apply with the viscosity η_(g) of the gas substituted for theviscosity η_(l) of the liquid.

In the case of bubble fragmentation it is known that each gas bubblerequires a deformation pressure drop $\begin{matrix}{{Ä\quad P_{d}} = \frac{4\quad á}{D}} & (3)\end{matrix}$to move along the channel 3, which is caused by the fact that the frontand rear surface of a bubble take on different shapes during movement ofthe bubble. In equation (3), α is a frictional surface tension parameterwhich must be established empirically, and D is the hydraulic diameterof the channel. Thus, the pressure drop ΔP_(b) required to drive abubble along the channel 3 will be the sum of the viscous anddeformation pressure drops: $\begin{matrix}{{Ä\quad P_{b}} = {\frac{4\quad á}{D} + \frac{128Q\quad ç_{g}L_{b}}{\partial D^{4}}}} & (4)\end{matrix}$wherein L_(b) is the length of channel taken up by the bubble. On theother hand, because a gas bubble replaces a plug of liquid of the samelength and the viscosity of gas is generally lower than the viscosity ofliquid, a gas bubble may flow more easily through the channel 3 than aplug of liquid of the same length. Combining equations (2) and (4), thereplacement a plug of liquid with a gas bubble leads to no change in thepressure drop if: $\begin{matrix}{{Ä( {Ä\quad P} )} = {{{- \frac{128Q\quad ç_{1}L_{b}}{\partial D^{4}}} + \frac{128Q\quad ç_{g}L_{b}}{\partial D^{4}} + \frac{4\quad á}{D}} = 0}} & (5)\end{matrix}$wherein L_(b) is again the length of the bubble which replaces a plug ofliquid of equal length. In equation (5), if Δ(ΔP)>0, the insertion of abubble increases the pressure drop, which leads to a risk of cloggingthe flow channel 3 with bubbles, whereas if Δ(ΔP)<0, the insertion of abubble reduces the pressure drop and poses no risk to the continued flowthrough the channel.

Rearranging equation (5) we define a limiting bubble length L_(bl), as$\begin{matrix}{L_{bl} = {\frac{{\partial á}\quad D^{3}}{32{Q( {ç_{1} - ç_{g}} )}}.}} & (6)\end{matrix}$Bubbles shorter than indicated by expression (6) lead to a risk ofclogging the flow channel because the gain from lower viscosity of thegas is offset by the loss due to deformation; bubbles longer thanindicated by expression (6) will flow freely along the flow channelbecause the gain from lower viscosity of the gas dominates.

Whether actual clogging will occur depends, of course, on the pressuremargin which is available for driving the flow. Clogging will occur onlyif the total pressure differential between the source 12 and therecipient 13 is consumed by the sum of pressure drops from a train ofbubbles and liquid plugs, according to equations (2) and (4).

As mentioned earlier, the occurrence of bubble fragmentation isunpredictable in flow restrictors of the simple configuration shown inFIG. 1. Investigation has shown, however, that the flow restrictorgeometry may be modified to suppress the generation of bubbles belowcritical length. One example of such a modified geometry is shown inFIG. 2.

Shown in FIG. 2, on a larger scale than in FIG. 1, is the inlet end of aflow restrictor of a similar overall construction as in FIG. 1. There isa difference, however, in that the flow channel 3 has been smoothly andgradually widened at the inlet to form a trombone-shaped inlet mouth.Near the inlet face 7, the channel is wide. Further away from the inletface the channel narrows down toward the original internal diameter D.In terms of the coordinate z set at zero at the inlet face 7 andpointing in the direction of flow as indicated at 22, at z=D the channelhas an internal diameter D(z)=3.5D, and at z=10.5 D the channel has aninternal diameter D(z)=D.

A first rule for the widening of the channel 3 may be derived from thecondition that the inlet geometry should at least allow the formation ofbubbles long enough to avoid blocking of the channel 3. Letting N denotethe number of bubbles present in the flow restrictor, flow will not beblocked ifNΔP _(d) <ÄP  (7)wherein ΔP_(d) denotes the deformation pressure drop of each bubble asdefined in (3) above. We now consider the pinch-off of a bubble in thewidened part of the flow channel 3 at a point where the channel has aninternal diameter D*>D. The volume of a bubble of length L_(min)=πD* atthis point can be approximated as $\begin{matrix}{V_{b} = {{{\partial D^{*}}\frac{\partial}{4}D^{*2}} = {\frac{\partial^{2}}{4}D^{*3}}}} & (8)\end{matrix}$

The maximum number N of such bubbles in a flow channel of length L isequal to the volume of the channel divided by the volume of a bubble:$\begin{matrix}{N = {\frac{\frac{\partial}{4}D^{2}L}{\frac{\partial^{2}}{4}D^{*3}} = \frac{{LD}^{2}}{\partial D^{*3}}}} & (9)\end{matrix}$By entering the expression (10) in expression (7) and combining with (2)and (3) above, we get $\begin{matrix}{{\frac{{LD}^{2}}{\partial D^{*3}}\frac{4á}{D}} < \frac{128Q\quad ç_{1}L}{D^{4}}} & (10)\end{matrix}$which can be rearranged to give $\begin{matrix}{D^{*} > \sqrt[3]{\frac{á\quad D^{5}}{32\quad ç\quad Q}}} & (11)\end{matrix}$

The physical interpretation of this expression is the following: If theinlet of the channel 3 is widened to a diameter slightly above D*, thisat least creates the possibility that bubbles produced by fragmentationwill be long enough to not completely stop the flow through the channel,even if the channel is filled up completely by such bubbles.

Turning now to our study of the fragmentation process itself, FIG. 2shows a bubble 16 of gas 15 entering the channel 3. At the front 23 ofthe bubble, liquid is displaced by the gas to form a thin film 17 ofthickness h(z) on the inner surface of the channel 3. Due the surfacetension at the gas-to-liquid interface 24, the film 17 is unstable. Thesurface tension exerts a pumping action causing a tendency of the liquidto flow both radially and axially, as shown at 25, which is a well-knownphenomenon in the field of hydrodynamics. This causes local accumulationof liquid which may eventually lead to the formation of a plug of liquidwhich fills the channel 3. Thus a smaller bubble 18 (not shown in FIG.2) may be pinched off from the bubble 16.

Our investigations indicate that it is largely a matter of local surfacecurvature and timing whether pinch-off will actually occur or not. Ifthe bubble 16 passes a site 25 of beginning local accumulation of liquidbut the liquid film 17 does not reach sufficient thickness to form aliquid plug while the bubble passes, pinch-off will not happen. On theother hand, if the liquid film 17 grows thick enough to coalesce at thecenter of the channel 3 to form a liquid plug while the bubble 16 flowspast the site 25, pinch-off will be the result.

Based on this it has now been found that by suitably widening the inletof the flow channel dependent on the desired flow rate, it is possibleto control the timing of perturbation growth of the liquid film aroundgas bubbles in the channel 3 in such a manner that any bubblefragmentation will lead to bubbles which are either longer than thelimiting length of equation 6 and thus pose no risk of blocking thecapillary, or short enough to reduce the flow but not numerous enough tostop the flow of liquid through the capillary.

From experimental and numerical studies it is known that a bubble movingalong a straight capillary with the bubble velocity v(z) will besurrounded by a liquid film of thickness $\begin{matrix}{{h(z)} = {( \frac{{v(z)}ç_{1}}{\overset{\sim}{a}} )^{\frac{2}{3}}{R(z)}}} & (12)\end{matrix}$wherein γ is the surface tension at the liquid-gas interface. As onewould expect, a slowly moving bubble is surrounded by a thinner film ofliquid than a fast-moving bubble. In case of standstill, a bubble willeventually displace all surrounding liquid and dry out the surface ofthe channel around it.

It may be said without making too much of an error that any bubble 18moves with the same velocity as the surrounding liquid. Therefore$\begin{matrix}{{v(z)} = \frac{Q}{\partial{R(z)}^{2}}} & (13)\end{matrix}$wherein v(z) denotes the velocity of a bubble at the location z. For abubble of length L_(b) this leads to a bubble transit time τ_(b) at thelocation z ofô _(b)(z)=L _(b) /v(z).  (14)

Bubble velocity has a characteristic (maximum) value v* at somecoordinate z along the channel 3 where R(z) is at its minimum.Accordingly, bubble transit time has a characteristic (minimum) valueτ_(b) withô _(b) =L _(b) /v*  (15)

It is not only bubble velocity, however, which determines the filmthickness. Since the liquid film adheres to the channel surface, itfollows the surface closely. Film thickness can be influenced bycontrolling the shape of the channel surface.

As shown in FIG. 2 at 26, the channel surface at any coordinate z withinthe widened channel portion slopes inward with a slope defined as$\begin{matrix}{{a(z)} = {- \frac{\mathbb{d}{R(z)}}{\mathbb{d}z}}} & (16)\end{matrix}$and has a tangent at z with the corresponding tapering angleè _(T)(z)=arctan(a(z))  (17)relative to the longitudinal axis of the channel 3, as shown at 27 inFIG. 2. In a similar fashion as with the bubble velocity and transittime above, we define the maximum tapering angle in the capillary inletas θ_(T)*.It has been found that within the tapered channel portion, instabilitieswill typically cause a liquid film of thickness h(z) to coalesce at thecenter of the flow channel, and thereby to pinch off a bubble, within alocal time period τ_(p)(z) of $\begin{matrix}{{{\hat{o}}_{p}(z)} = {\frac{0.01}{( è_{T}^{*} )^{1.2}}( \frac{R(z)}{h(z)} )^{3}{\frac{3ç_{1}{R(z)}}{\overset{\sim}{a}}.}}} & (18)\end{matrix}$

Our investigations indicate that the smallest of these local timeperiods, referred to as τ*, governs the time scale of bubblesegmentation within the widened part of the channel 3.

As it is desired to prevent bubble fragmentation into bubbles shorterthan the limiting bubble length given in equation (6), and thecharacteristic (minimum) transit time τ_(bl) of such bubbles isô _(bl) =L _(bl) /v*,  (19)a channel slope designed such thatô*>ô_(bl)  (20)will prevent the formation of bubbles having a length L_(b)<L_(bl).

Relations (11) and (20) may then be combined in the design of thewidened inlet to the channel 3 to form a flow restrictor which istolerant to bubble fragmentation, as follows:

In a first section of the channel 3 between the inlet face 7 and a firstz-coordinate z₁, the channel diameter D should be kept larger than thevalue D* given by relation (11) above. In this connection, thecoordinate z₁ is defined as the first location along the channel wherethe channel diameter narrows down to D*. This will ensure that anybubble segmentation within the first section does not generate bubbleswhich are so short as to block the flow completely.

In a second section of the channel, between the z-coordinate z₁ and asecond z-coordinate z₂, the channel should be designed to narrow downgradually towards the original channel diameter D in accordance with therelation (20) above. The second z-coordinate z₂ is defined as the firstlocation along the channel where the channel narrows down to itsoriginal, overall diameter D. In practical terms this means that thegeometry should be designed to minimize the change in surface curvatureas the channel narrows down. This will ensure that bubbles which havereached z₁ unfragmented, or which have been fragmented at z₁ intobubbles of non-critical length, will not be further fragmented duringtheir passage along the second channel section, and will enter into theremaining, straight section of channel 3 unfragmented and remainunfragmented also there.

We reserve the right to claim flow restrictors designed in accordancewith relation (11), relation (20) or both, or any other relationdisclosed in this patent application or any physical interpretation ofany such relation. The embodiment shown in the drawings should beconsidered in a non-limiting fashion as being exemplary of a preferredway of practising the invention. As an alternative, flow restrictors ofa similar nature may be made in planar technology by micromachining orembossing techniques, for example. In such realisations, it might beenvisioned to connect several flow restrictors in series or parallel forspecific purposes.

While the present invention has been illustrated and described withrespect to a particular embodiment thereof, it should be appreciated bythose of ordinary skill in the art that various modifications to thisinvention may be made without departing from the spirit and scope of thepresent invention.

1-8. (canceled)
 9. A flow restrictor for restricting a flow of liquid,the restrictor comprising a body with an inlet face, an outlet face anda flow channel extending therebetween from an inlet to an outlet, thechannel having over most of its length a diameter D, wherein the flowchannel has been widened at least at the inlet in such a manner that atdistances z from the inlet face: at z=D the channel has an internaldiameter D(z)=3.5D, and at z≧10.5D the channel has an internal diameterD(z)=D, and in such a manner that internal diameter, D(z), is narrowedsmoothly and gradually as a function of z.
 10. The flow restrictoraccording to claim 9, wherein the geometry of the flow channel isdesigned to minimize the change in curvature in the widened part of theflow channel.
 11. An apparatus for delivering a restricted flow ofliquid to a recipient, the apparatus comprising a reservoir of liquid athigher pressure than the recipient, a flow restrictor as claimed in anypreceding claim, a transfer conduit in fluid communication with thereservoir and the inlet of the restrictor, and a delivery conduit influid communication with the outlet of the restrictor and the recipient.